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FA-67851 / Traffic signal timing plans / Open access

Webster cycle length: the constant 5 s is scaled together with lost time · case 01

Webster cycle length returns a wrong result when the constant 5 s is scaled together with lost time.

Verified by executionVariant 1 · 8 checks per implementationDownload source bundle ↓JSON ↗

ROOT CAUSE

Parenthesization multiplies the 5 second constant by 1.5, lengthening every computed cycle.

VERIFIED REPAIR

Restore the Webster numerator rule so that the step reads `(Fraction(3, 2) * L + 5)`.

Unsuccessful approach: Multiplying the constant by the number of phases is a different wrong scaling of the same fixed term.

Case contract

Input {phases: per-phase lists of lane-group flows veh/h, sat: saturation flow per lane group, lost: lost seconds per phase, allred: extra all-red seconds per cycle, cmin, cmax}. Y is the sum over phases of the critical (largest) flow ratio; L = lost*phases + allred. If Y >= 0.9 return 'oversaturated'. Otherwise C0 = (1.5L + 5)/(1 - Y), rounded UP to a multiple of 5 s and clamped to [cmin, cmax]. Return {cycle, lost: L, y_milli: floor(1000Y)}.

Why this case matters

Signal timing arithmetic is exact and integer or rational; a wrong rule silently produces unsafe or inefficient timing plans.

1 / The failure

Exit 1
"""Failure Map reference implementation. Python standard library only."""
import json
from fractions import Fraction
import math
N = 1
observations = []
def solve(x):
    ph = x['phases']
    s = x['sat']
    Y = Fraction(0)
    for group in ph:
        Y += Fraction(max(group), s)
    L = x['lost'] * len(ph) + x['allred']
    if Y >= Fraction(9, 10):
        return 'oversaturated'
    c0 = (Fraction(3, 2) * (L + 5)) / (1 - Y)
    c = -(-c0 // 5) * 5
    c = max(x['cmin'], min(x['cmax'], int(c)))
    return {'cycle': c, 'lost': L, 'y_milli': int(Y * 1000)}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[({'phases': [[840, 390], [810]], 'sat': 2000, 'lost': 3, 'allred': 1, 'cmin': 40, 'cmax': 150}, {'cycle': 90, 'lost': 7, 'y_milli': 825}), ({'phases': [[510], [450, 510, 660], [300]], 'sat': 1800, 'lost': 5, 'allred': 3, 'cmin': 50, 'cmax': 180}, {'cycle': 175, 'lost': 18, 'y_milli': 816}), ({'phases': [[810], [810]], 'sat': 1800, 'lost': 4, 'allred': 0, 'cmin': 40, 'cmax': 180}, 'oversaturated'), ({'phases': [[90], [90], [90]], 'sat': 1800, 'lost': 3, 'allred': 0, 'cmin': 60, 'cmax': 120}, {'cycle': 60, 'lost': 9, 'y_milli': 150}), ({'phases': [[660, 840, 750], [90, 150]], 'sat': 1800, 'lost': 3, 'allred': 1, 'cmin': 40, 'cmax': 90}, {'cycle': 40, 'lost': 7, 'y_milli': 550}), ({'phases': [[660, 870, 540], [270, 750, 900], [390, 510, 630], [570]], 'sat': 2000, 'lost': 5, 'allred': 5, 'cmin': 50, 'cmax': 120}, 'oversaturated'), ({'phases': [[300, 540, 240], [420, 480, 690]], 'sat': 1800, 'lost': 2, 'allred': 1, 'cmin': 40, 'cmax': 90}, {'cycle': 40, 'lost': 5, 'y_milli': 683}), ({'phases': [[720, 360], [540, 900]], 'sat': 1800, 'lost': 4, 'allred': 4, 'cmin': 60, 'cmax': 150}, 'oversaturated')], [({'phases': [[300, 480], [540, 300, 900], [480, 210], [390]], 'sat': 1800, 'lost': 5, 'allred': 2, 'cmin': 60, 'cmax': 150}, 'oversaturated'), ({'phases': [[720, 360], [540, 900]], 'sat': 1800, 'lost': 4, 'allred': 4, 'cmin': 60, 'cmax': 150}, 'oversaturated'), ({'phases': [[630], [630, 240], [60]], 'sat': 2000, 'lost': 5, 'allred': 1, 'cmin': 60, 'cmax': 180}, {'cycle': 90, 'lost': 16, 'y_milli': 660}), ({'phases': [[90], [90], [90]], 'sat': 1800, 'lost': 3, 'allred': 0, 'cmin': 60, 'cmax': 120}, {'cycle': 60, 'lost': 9, 'y_milli': 150}), ({'phases': [[270], [240, 420], [570, 510], [660]], 'sat': 1900, 'lost': 3, 'allred': 6, 'cmin': 40, 'cmax': 150}, 'oversaturated'), ({'phases': [[90, 540], [720, 600, 720]], 'sat': 1800, 'lost': 2, 'allred': 2, 'cmin': 40, 'cmax': 150}, {'cycle': 50, 'lost': 6, 'y_milli': 700}), ({'phases': [[300, 600], [450]], 'sat': 1800, 'lost': 4, 'allred': 2, 'cmin': 40, 'cmax': 120}, {'cycle': 50, 'lost': 10, 'y_milli': 583}), ({'phases': [[120, 900], [390, 720, 450], [450, 510]], 'sat': 1900, 'lost': 2, 'allred': 0, 'cmin': 50, 'cmax': 180}, 'oversaturated')], [({'phases': [[210, 870, 390], [390, 270], [60, 60, 360]], 'sat': 1800, 'lost': 5, 'allred': 4, 'cmin': 40, 'cmax': 120}, 'oversaturated'), ({'phases': [[780, 120, 780], [270]], 'sat': 1900, 'lost': 4, 'allred': 6, 'cmin': 60, 'cmax': 120}, {'cycle': 60, 'lost': 14, 'y_milli': 552}), ({'phases': [[210], [210, 810, 540]], 'sat': 1800, 'lost': 5, 'allred': 5, 'cmin': 40, 'cmax': 90}, {'cycle': 65, 'lost': 15, 'y_milli': 566}), ({'phases': [[900], [390, 60, 450]], 'sat': 1800, 'lost': 5, 'allred': 5, 'cmin': 60, 'cmax': 90}, {'cycle': 90, 'lost': 15, 'y_milli': 750}), ({'phases': [[810], [810]], 'sat': 1800, 'lost': 4, 'allred': 0, 'cmin': 40, 'cmax': 180}, 'oversaturated'), ({'phases': [[90], [90], [90]], 'sat': 1800, 'lost': 3, 'allred': 0, 'cmin': 60, 'cmax': 120}, {'cycle': 60, 'lost': 9, 'y_milli': 150}), ({'phases': [[450, 870], [300, 420, 150]], 'sat': 1900, 'lost': 3, 'allred': 2, 'cmin': 60, 'cmax': 90}, {'cycle': 60, 'lost': 8, 'y_milli': 678}), ({'phases': [[720, 360], [540, 900]], 'sat': 1800, 'lost': 4, 'allred': 4, 'cmin': 60, 'cmax': 150}, 'oversaturated')], [({'phases': [[480], [210]], 'sat': 1800, 'lost': 2, 'allred': 6, 'cmin': 60, 'cmax': 90}, {'cycle': 60, 'lost': 10, 'y_milli': 383}), ({'phases': [[660, 210], [270, 900, 180]], 'sat': 1900, 'lost': 5, 'allred': 4, 'cmin': 40, 'cmax': 180}, {'cycle': 150, 'lost': 14, 'y_milli': 821}), ({'phases': [[720, 360], [540, 900]], 'sat': 1800, 'lost': 4, 'allred': 4, 'cmin': 60, 'cmax': 150}, 'oversaturated'), ({'phases': [[300, 600], [450]], 'sat': 1800, 'lost': 4, 'allred': 2, 'cmin': 40, 'cmax': 120}, {'cycle': 50, 'lost': 10, 'y_milli': 583}), ({'phases': [[810], [810]], 'sat': 1800, 'lost': 4, 'allred': 0, 'cmin': 40, 'cmax': 180}, 'oversaturated'), ({'phases': [[540, 450, 360], [720, 210, 390], [360]], 'sat': 1800, 'lost': 4, 'allred': 0, 'cmin': 60, 'cmax': 180}, 'oversaturated'), ({'phases': [[660, 360, 450], [630], [870, 210, 120], [720]], 'sat': 1900, 'lost': 4, 'allred': 1, 'cmin': 50, 'cmax': 90}, 'oversaturated'), ({'phases': [[420], [150], [60, 360, 510]], 'sat': 1800, 'lost': 5, 'allred': 2, 'cmin': 40, 'cmax': 120}, {'cycle': 80, 'lost': 17, 'y_milli': 600})], [({'phases': [[720, 360], [540, 900]], 'sat': 1800, 'lost': 4, 'allred': 4, 'cmin': 60, 'cmax': 150}, 'oversaturated'), ({'phases': [[690], [750, 750]], 'sat': 1900, 'lost': 3, 'allred': 4, 'cmin': 60, 'cmax': 150}, {'cycle': 85, 'lost': 10, 'y_milli': 757}), ({'phases': [[810], [810]], 'sat': 1800, 'lost': 4, 'allred': 0, 'cmin': 40, 'cmax': 180}, 'oversaturated'), ({'phases': [[210], [390, 660], [210, 480, 210]], 'sat': 1800, 'lost': 3, 'allred': 1, 'cmin': 50, 'cmax': 90}, {'cycle': 80, 'lost': 10, 'y_milli': 750}), ({'phases': [[720, 600, 330], [480]], 'sat': 1900, 'lost': 2, 'allred': 1, 'cmin': 40, 'cmax': 180}, {'cycle': 40, 'lost': 5, 'y_milli': 631}), ({'phases': [[90], [90], [90]], 'sat': 1800, 'lost': 3, 'allred': 0, 'cmin': 60, 'cmax': 120}, {'cycle': 60, 'lost': 9, 'y_milli': 150}), ({'phases': [[810], [810, 360], [180]], 'sat': 1900, 'lost': 5, 'allred': 6, 'cmin': 40, 'cmax': 120}, 'oversaturated'), ({'phases': [[420, 420], [150, 300, 750], [540, 150], [510]], 'sat': 1800, 'lost': 5, 'allred': 1, 'cmin': 50, 'cmax': 180}, 'oversaturated')]]
for i, (args, expected) in enumerate(fixtures[N-1]):
    check('timing oracle' + ' %d' % i, solve(args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)
Boundary fixtureActualExpectedOutcome
timing oracle 0{'cycle': 105, 'lost': 7, 'y_milli': 825}{'cycle': 90, 'lost': 7, 'y_milli': 825}Failed
timing oracle 1{'cycle': 180, 'lost': 18, 'y_milli': 816}{'cycle': 175, 'lost': 18, 'y_milli': 816}Failed
timing oracle 2oversaturatedoversaturatedPassed
timing oracle 3{'cycle': 60, 'lost': 9, 'y_milli': 150}{'cycle': 60, 'lost': 9, 'y_milli': 150}Passed
timing oracle 4{'cycle': 40, 'lost': 7, 'y_milli': 550}{'cycle': 40, 'lost': 7, 'y_milli': 550}Passed
timing oracle 5oversaturatedoversaturatedPassed
timing oracle 6{'cycle': 50, 'lost': 5, 'y_milli': 683}{'cycle': 40, 'lost': 5, 'y_milli': 683}Failed
timing oracle 7oversaturatedoversaturatedPassed

SHA-256 / 2b036323df1520a5f2e53b4b6218ff88148d466a10cab2d3d9475b8b2aa81195

2 / The unsuccessful fix

Exit 1
"""Failure Map reference implementation. Python standard library only."""
import json
from fractions import Fraction
import math
N = 1
observations = []
def solve(x):
    ph = x['phases']
    s = x['sat']
    Y = Fraction(0)
    for group in ph:
        Y += Fraction(max(group), s)
    L = x['lost'] * len(ph) + x['allred']
    if Y >= Fraction(9, 10):
        return 'oversaturated'
    c0 = (Fraction(3, 2) * L + 5 * len(ph)) / (1 - Y)
    c = -(-c0 // 5) * 5
    c = max(x['cmin'], min(x['cmax'], int(c)))
    return {'cycle': c, 'lost': L, 'y_milli': int(Y * 1000)}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[({'phases': [[840, 390], [810]], 'sat': 2000, 'lost': 3, 'allred': 1, 'cmin': 40, 'cmax': 150}, {'cycle': 90, 'lost': 7, 'y_milli': 825}), ({'phases': [[510], [450, 510, 660], [300]], 'sat': 1800, 'lost': 5, 'allred': 3, 'cmin': 50, 'cmax': 180}, {'cycle': 175, 'lost': 18, 'y_milli': 816}), ({'phases': [[810], [810]], 'sat': 1800, 'lost': 4, 'allred': 0, 'cmin': 40, 'cmax': 180}, 'oversaturated'), ({'phases': [[90], [90], [90]], 'sat': 1800, 'lost': 3, 'allred': 0, 'cmin': 60, 'cmax': 120}, {'cycle': 60, 'lost': 9, 'y_milli': 150}), ({'phases': [[660, 840, 750], [90, 150]], 'sat': 1800, 'lost': 3, 'allred': 1, 'cmin': 40, 'cmax': 90}, {'cycle': 40, 'lost': 7, 'y_milli': 550}), ({'phases': [[660, 870, 540], [270, 750, 900], [390, 510, 630], [570]], 'sat': 2000, 'lost': 5, 'allred': 5, 'cmin': 50, 'cmax': 120}, 'oversaturated'), ({'phases': [[300, 540, 240], [420, 480, 690]], 'sat': 1800, 'lost': 2, 'allred': 1, 'cmin': 40, 'cmax': 90}, {'cycle': 40, 'lost': 5, 'y_milli': 683}), ({'phases': [[720, 360], [540, 900]], 'sat': 1800, 'lost': 4, 'allred': 4, 'cmin': 60, 'cmax': 150}, 'oversaturated')], [({'phases': [[300, 480], [540, 300, 900], [480, 210], [390]], 'sat': 1800, 'lost': 5, 'allred': 2, 'cmin': 60, 'cmax': 150}, 'oversaturated'), ({'phases': [[720, 360], [540, 900]], 'sat': 1800, 'lost': 4, 'allred': 4, 'cmin': 60, 'cmax': 150}, 'oversaturated'), ({'phases': [[630], [630, 240], [60]], 'sat': 2000, 'lost': 5, 'allred': 1, 'cmin': 60, 'cmax': 180}, {'cycle': 90, 'lost': 16, 'y_milli': 660}), ({'phases': [[90], [90], [90]], 'sat': 1800, 'lost': 3, 'allred': 0, 'cmin': 60, 'cmax': 120}, {'cycle': 60, 'lost': 9, 'y_milli': 150}), ({'phases': [[270], [240, 420], [570, 510], [660]], 'sat': 1900, 'lost': 3, 'allred': 6, 'cmin': 40, 'cmax': 150}, 'oversaturated'), ({'phases': [[90, 540], [720, 600, 720]], 'sat': 1800, 'lost': 2, 'allred': 2, 'cmin': 40, 'cmax': 150}, {'cycle': 50, 'lost': 6, 'y_milli': 700}), ({'phases': [[300, 600], [450]], 'sat': 1800, 'lost': 4, 'allred': 2, 'cmin': 40, 'cmax': 120}, {'cycle': 50, 'lost': 10, 'y_milli': 583}), ({'phases': [[120, 900], [390, 720, 450], [450, 510]], 'sat': 1900, 'lost': 2, 'allred': 0, 'cmin': 50, 'cmax': 180}, 'oversaturated')], [({'phases': [[210, 870, 390], [390, 270], [60, 60, 360]], 'sat': 1800, 'lost': 5, 'allred': 4, 'cmin': 40, 'cmax': 120}, 'oversaturated'), ({'phases': [[780, 120, 780], [270]], 'sat': 1900, 'lost': 4, 'allred': 6, 'cmin': 60, 'cmax': 120}, {'cycle': 60, 'lost': 14, 'y_milli': 552}), ({'phases': [[210], [210, 810, 540]], 'sat': 1800, 'lost': 5, 'allred': 5, 'cmin': 40, 'cmax': 90}, {'cycle': 65, 'lost': 15, 'y_milli': 566}), ({'phases': [[900], [390, 60, 450]], 'sat': 1800, 'lost': 5, 'allred': 5, 'cmin': 60, 'cmax': 90}, {'cycle': 90, 'lost': 15, 'y_milli': 750}), ({'phases': [[810], [810]], 'sat': 1800, 'lost': 4, 'allred': 0, 'cmin': 40, 'cmax': 180}, 'oversaturated'), ({'phases': [[90], [90], [90]], 'sat': 1800, 'lost': 3, 'allred': 0, 'cmin': 60, 'cmax': 120}, {'cycle': 60, 'lost': 9, 'y_milli': 150}), ({'phases': [[450, 870], [300, 420, 150]], 'sat': 1900, 'lost': 3, 'allred': 2, 'cmin': 60, 'cmax': 90}, {'cycle': 60, 'lost': 8, 'y_milli': 678}), ({'phases': [[720, 360], [540, 900]], 'sat': 1800, 'lost': 4, 'allred': 4, 'cmin': 60, 'cmax': 150}, 'oversaturated')], [({'phases': [[480], [210]], 'sat': 1800, 'lost': 2, 'allred': 6, 'cmin': 60, 'cmax': 90}, {'cycle': 60, 'lost': 10, 'y_milli': 383}), ({'phases': [[660, 210], [270, 900, 180]], 'sat': 1900, 'lost': 5, 'allred': 4, 'cmin': 40, 'cmax': 180}, {'cycle': 150, 'lost': 14, 'y_milli': 821}), ({'phases': [[720, 360], [540, 900]], 'sat': 1800, 'lost': 4, 'allred': 4, 'cmin': 60, 'cmax': 150}, 'oversaturated'), ({'phases': [[300, 600], [450]], 'sat': 1800, 'lost': 4, 'allred': 2, 'cmin': 40, 'cmax': 120}, {'cycle': 50, 'lost': 10, 'y_milli': 583}), ({'phases': [[810], [810]], 'sat': 1800, 'lost': 4, 'allred': 0, 'cmin': 40, 'cmax': 180}, 'oversaturated'), ({'phases': [[540, 450, 360], [720, 210, 390], [360]], 'sat': 1800, 'lost': 4, 'allred': 0, 'cmin': 60, 'cmax': 180}, 'oversaturated'), ({'phases': [[660, 360, 450], [630], [870, 210, 120], [720]], 'sat': 1900, 'lost': 4, 'allred': 1, 'cmin': 50, 'cmax': 90}, 'oversaturated'), ({'phases': [[420], [150], [60, 360, 510]], 'sat': 1800, 'lost': 5, 'allred': 2, 'cmin': 40, 'cmax': 120}, {'cycle': 80, 'lost': 17, 'y_milli': 600})], [({'phases': [[720, 360], [540, 900]], 'sat': 1800, 'lost': 4, 'allred': 4, 'cmin': 60, 'cmax': 150}, 'oversaturated'), ({'phases': [[690], [750, 750]], 'sat': 1900, 'lost': 3, 'allred': 4, 'cmin': 60, 'cmax': 150}, {'cycle': 85, 'lost': 10, 'y_milli': 757}), ({'phases': [[810], [810]], 'sat': 1800, 'lost': 4, 'allred': 0, 'cmin': 40, 'cmax': 180}, 'oversaturated'), ({'phases': [[210], [390, 660], [210, 480, 210]], 'sat': 1800, 'lost': 3, 'allred': 1, 'cmin': 50, 'cmax': 90}, {'cycle': 80, 'lost': 10, 'y_milli': 750}), ({'phases': [[720, 600, 330], [480]], 'sat': 1900, 'lost': 2, 'allred': 1, 'cmin': 40, 'cmax': 180}, {'cycle': 40, 'lost': 5, 'y_milli': 631}), ({'phases': [[90], [90], [90]], 'sat': 1800, 'lost': 3, 'allred': 0, 'cmin': 60, 'cmax': 120}, {'cycle': 60, 'lost': 9, 'y_milli': 150}), ({'phases': [[810], [810, 360], [180]], 'sat': 1900, 'lost': 5, 'allred': 6, 'cmin': 40, 'cmax': 120}, 'oversaturated'), ({'phases': [[420, 420], [150, 300, 750], [540, 150], [510]], 'sat': 1800, 'lost': 5, 'allred': 1, 'cmin': 50, 'cmax': 180}, 'oversaturated')]]
for i, (args, expected) in enumerate(fixtures[N-1]):
    check('timing oracle' + ' %d' % i, solve(args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)
Boundary fixtureActualExpectedOutcome
timing oracle 0{'cycle': 120, 'lost': 7, 'y_milli': 825}{'cycle': 90, 'lost': 7, 'y_milli': 825}Failed
timing oracle 1{'cycle': 180, 'lost': 18, 'y_milli': 816}{'cycle': 175, 'lost': 18, 'y_milli': 816}Failed
timing oracle 2oversaturatedoversaturatedPassed
timing oracle 3{'cycle': 60, 'lost': 9, 'y_milli': 150}{'cycle': 60, 'lost': 9, 'y_milli': 150}Passed
timing oracle 4{'cycle': 50, 'lost': 7, 'y_milli': 550}{'cycle': 40, 'lost': 7, 'y_milli': 550}Failed
timing oracle 5oversaturatedoversaturatedPassed
timing oracle 6{'cycle': 60, 'lost': 5, 'y_milli': 683}{'cycle': 40, 'lost': 5, 'y_milli': 683}Failed
timing oracle 7oversaturatedoversaturatedPassed

SHA-256 / fb8e58d1c2f8c73fe858150e4720593effa32bb71c7a7ad87f1b0dab82be9ec6

3 / The verified repair

Exit 0
"""Failure Map reference implementation. Python standard library only."""
import json
from fractions import Fraction
import math
N = 1
observations = []
def solve(x):
    ph = x['phases']
    s = x['sat']
    Y = Fraction(0)
    for group in ph:
        Y += Fraction(max(group), s)
    L = x['lost'] * len(ph) + x['allred']
    if Y >= Fraction(9, 10):
        return 'oversaturated'
    c0 = (Fraction(3, 2) * L + 5) / (1 - Y)
    c = -(-c0 // 5) * 5
    c = max(x['cmin'], min(x['cmax'], int(c)))
    return {'cycle': c, 'lost': L, 'y_milli': int(Y * 1000)}
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[({'phases': [[840, 390], [810]], 'sat': 2000, 'lost': 3, 'allred': 1, 'cmin': 40, 'cmax': 150}, {'cycle': 90, 'lost': 7, 'y_milli': 825}), ({'phases': [[510], [450, 510, 660], [300]], 'sat': 1800, 'lost': 5, 'allred': 3, 'cmin': 50, 'cmax': 180}, {'cycle': 175, 'lost': 18, 'y_milli': 816}), ({'phases': [[810], [810]], 'sat': 1800, 'lost': 4, 'allred': 0, 'cmin': 40, 'cmax': 180}, 'oversaturated'), ({'phases': [[90], [90], [90]], 'sat': 1800, 'lost': 3, 'allred': 0, 'cmin': 60, 'cmax': 120}, {'cycle': 60, 'lost': 9, 'y_milli': 150}), ({'phases': [[660, 840, 750], [90, 150]], 'sat': 1800, 'lost': 3, 'allred': 1, 'cmin': 40, 'cmax': 90}, {'cycle': 40, 'lost': 7, 'y_milli': 550}), ({'phases': [[660, 870, 540], [270, 750, 900], [390, 510, 630], [570]], 'sat': 2000, 'lost': 5, 'allred': 5, 'cmin': 50, 'cmax': 120}, 'oversaturated'), ({'phases': [[300, 540, 240], [420, 480, 690]], 'sat': 1800, 'lost': 2, 'allred': 1, 'cmin': 40, 'cmax': 90}, {'cycle': 40, 'lost': 5, 'y_milli': 683}), ({'phases': [[720, 360], [540, 900]], 'sat': 1800, 'lost': 4, 'allred': 4, 'cmin': 60, 'cmax': 150}, 'oversaturated')], [({'phases': [[300, 480], [540, 300, 900], [480, 210], [390]], 'sat': 1800, 'lost': 5, 'allred': 2, 'cmin': 60, 'cmax': 150}, 'oversaturated'), ({'phases': [[720, 360], [540, 900]], 'sat': 1800, 'lost': 4, 'allred': 4, 'cmin': 60, 'cmax': 150}, 'oversaturated'), ({'phases': [[630], [630, 240], [60]], 'sat': 2000, 'lost': 5, 'allred': 1, 'cmin': 60, 'cmax': 180}, {'cycle': 90, 'lost': 16, 'y_milli': 660}), ({'phases': [[90], [90], [90]], 'sat': 1800, 'lost': 3, 'allred': 0, 'cmin': 60, 'cmax': 120}, {'cycle': 60, 'lost': 9, 'y_milli': 150}), ({'phases': [[270], [240, 420], [570, 510], [660]], 'sat': 1900, 'lost': 3, 'allred': 6, 'cmin': 40, 'cmax': 150}, 'oversaturated'), ({'phases': [[90, 540], [720, 600, 720]], 'sat': 1800, 'lost': 2, 'allred': 2, 'cmin': 40, 'cmax': 150}, {'cycle': 50, 'lost': 6, 'y_milli': 700}), ({'phases': [[300, 600], [450]], 'sat': 1800, 'lost': 4, 'allred': 2, 'cmin': 40, 'cmax': 120}, {'cycle': 50, 'lost': 10, 'y_milli': 583}), ({'phases': [[120, 900], [390, 720, 450], [450, 510]], 'sat': 1900, 'lost': 2, 'allred': 0, 'cmin': 50, 'cmax': 180}, 'oversaturated')], [({'phases': [[210, 870, 390], [390, 270], [60, 60, 360]], 'sat': 1800, 'lost': 5, 'allred': 4, 'cmin': 40, 'cmax': 120}, 'oversaturated'), ({'phases': [[780, 120, 780], [270]], 'sat': 1900, 'lost': 4, 'allred': 6, 'cmin': 60, 'cmax': 120}, {'cycle': 60, 'lost': 14, 'y_milli': 552}), ({'phases': [[210], [210, 810, 540]], 'sat': 1800, 'lost': 5, 'allred': 5, 'cmin': 40, 'cmax': 90}, {'cycle': 65, 'lost': 15, 'y_milli': 566}), ({'phases': [[900], [390, 60, 450]], 'sat': 1800, 'lost': 5, 'allred': 5, 'cmin': 60, 'cmax': 90}, {'cycle': 90, 'lost': 15, 'y_milli': 750}), ({'phases': [[810], [810]], 'sat': 1800, 'lost': 4, 'allred': 0, 'cmin': 40, 'cmax': 180}, 'oversaturated'), ({'phases': [[90], [90], [90]], 'sat': 1800, 'lost': 3, 'allred': 0, 'cmin': 60, 'cmax': 120}, {'cycle': 60, 'lost': 9, 'y_milli': 150}), ({'phases': [[450, 870], [300, 420, 150]], 'sat': 1900, 'lost': 3, 'allred': 2, 'cmin': 60, 'cmax': 90}, {'cycle': 60, 'lost': 8, 'y_milli': 678}), ({'phases': [[720, 360], [540, 900]], 'sat': 1800, 'lost': 4, 'allred': 4, 'cmin': 60, 'cmax': 150}, 'oversaturated')], [({'phases': [[480], [210]], 'sat': 1800, 'lost': 2, 'allred': 6, 'cmin': 60, 'cmax': 90}, {'cycle': 60, 'lost': 10, 'y_milli': 383}), ({'phases': [[660, 210], [270, 900, 180]], 'sat': 1900, 'lost': 5, 'allred': 4, 'cmin': 40, 'cmax': 180}, {'cycle': 150, 'lost': 14, 'y_milli': 821}), ({'phases': [[720, 360], [540, 900]], 'sat': 1800, 'lost': 4, 'allred': 4, 'cmin': 60, 'cmax': 150}, 'oversaturated'), ({'phases': [[300, 600], [450]], 'sat': 1800, 'lost': 4, 'allred': 2, 'cmin': 40, 'cmax': 120}, {'cycle': 50, 'lost': 10, 'y_milli': 583}), ({'phases': [[810], [810]], 'sat': 1800, 'lost': 4, 'allred': 0, 'cmin': 40, 'cmax': 180}, 'oversaturated'), ({'phases': [[540, 450, 360], [720, 210, 390], [360]], 'sat': 1800, 'lost': 4, 'allred': 0, 'cmin': 60, 'cmax': 180}, 'oversaturated'), ({'phases': [[660, 360, 450], [630], [870, 210, 120], [720]], 'sat': 1900, 'lost': 4, 'allred': 1, 'cmin': 50, 'cmax': 90}, 'oversaturated'), ({'phases': [[420], [150], [60, 360, 510]], 'sat': 1800, 'lost': 5, 'allred': 2, 'cmin': 40, 'cmax': 120}, {'cycle': 80, 'lost': 17, 'y_milli': 600})], [({'phases': [[720, 360], [540, 900]], 'sat': 1800, 'lost': 4, 'allred': 4, 'cmin': 60, 'cmax': 150}, 'oversaturated'), ({'phases': [[690], [750, 750]], 'sat': 1900, 'lost': 3, 'allred': 4, 'cmin': 60, 'cmax': 150}, {'cycle': 85, 'lost': 10, 'y_milli': 757}), ({'phases': [[810], [810]], 'sat': 1800, 'lost': 4, 'allred': 0, 'cmin': 40, 'cmax': 180}, 'oversaturated'), ({'phases': [[210], [390, 660], [210, 480, 210]], 'sat': 1800, 'lost': 3, 'allred': 1, 'cmin': 50, 'cmax': 90}, {'cycle': 80, 'lost': 10, 'y_milli': 750}), ({'phases': [[720, 600, 330], [480]], 'sat': 1900, 'lost': 2, 'allred': 1, 'cmin': 40, 'cmax': 180}, {'cycle': 40, 'lost': 5, 'y_milli': 631}), ({'phases': [[90], [90], [90]], 'sat': 1800, 'lost': 3, 'allred': 0, 'cmin': 60, 'cmax': 120}, {'cycle': 60, 'lost': 9, 'y_milli': 150}), ({'phases': [[810], [810, 360], [180]], 'sat': 1900, 'lost': 5, 'allred': 6, 'cmin': 40, 'cmax': 120}, 'oversaturated'), ({'phases': [[420, 420], [150, 300, 750], [540, 150], [510]], 'sat': 1800, 'lost': 5, 'allred': 1, 'cmin': 50, 'cmax': 180}, 'oversaturated')]]
for i, (args, expected) in enumerate(fixtures[N-1]):
    check('timing oracle' + ' %d' % i, solve(args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)
Boundary fixtureActualExpectedOutcome
timing oracle 0{'cycle': 90, 'lost': 7, 'y_milli': 825}{'cycle': 90, 'lost': 7, 'y_milli': 825}Passed
timing oracle 1{'cycle': 175, 'lost': 18, 'y_milli': 816}{'cycle': 175, 'lost': 18, 'y_milli': 816}Passed
timing oracle 2oversaturatedoversaturatedPassed
timing oracle 3{'cycle': 60, 'lost': 9, 'y_milli': 150}{'cycle': 60, 'lost': 9, 'y_milli': 150}Passed
timing oracle 4{'cycle': 40, 'lost': 7, 'y_milli': 550}{'cycle': 40, 'lost': 7, 'y_milli': 550}Passed
timing oracle 5oversaturatedoversaturatedPassed
timing oracle 6{'cycle': 40, 'lost': 5, 'y_milli': 683}{'cycle': 40, 'lost': 5, 'y_milli': 683}Passed
timing oracle 7oversaturatedoversaturatedPassed

SHA-256 / 3e1a218a875968ab3541bc6a84a325cc60d597ab938478071520a251c440ebda

Verification & scope

A deterministic, bounded toy model with a stipulated contract; it makes no claim of conformance to any agency manual or standard. This reproducer isolates one failure mechanism. Results cover the supplied fixtures. Variants within a family share a test contract and should remain grouped when constructing evaluation splits. Related mechanisms with a shared evaluation_group must also remain together; these controlled models are not independent production incidents.

Observations recorded using Python 3.12.14 at 2026-09-29T14:47:56.586548+00:00.

Case digest / 14fbf596e032796062eb31eec7d452c1a7759d630aef7616cd3e746e8be44a98